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A multi-objective optimization of oil well drilling has been carried out using a binary coded elitist non-dominated sorting genetic algorithm. A Louisiana offshore field with abnormal formation pressure is considered for optimization. Several multi-objective optimization problems involving twoand three-objective functions were formulated and solved to fix optimal drilling variables. The important objectives are: (i) maximizing drilling depth, (ii) minimizing drilling time and (iii) minimizing drilling cost with fractional drill bit tooth wear as a constraint. Important time dependent decision variables are: (i) equivalent circulation mud density, (ii) drill bit rotation, (iii) weight on bit and (iv) Reynolds number function of circulating mud through drill bit nozzles. A set of non-dominated optimal Pareto frontier is obtained for the two-objective optimization problem whereas a non-dominated optimal Pareto surface is obtained for the three-objective optimization problem. Depending on the trade-offs involved, decision makers may select any point from the optimal Pareto frontier or optimal Pareto surface and hence corresponding values of the decision variables that may be selected for optimal drilling operation. For minimizing drilling time and drilling cost, the optimum values of the decision variables are needed to be kept at the higher values whereas the optimum values of decision variables are at the lower values for the maximization of drilling depth.